SAT Question 096c7ef5: Area and Volume answer and explanation with Desmos solution

Choice B is correct. It’s given that the three points shown define a circle, so the center of that circle is an equal distance from each of the three points. The point $(7,8)$ is halfway between the points $(7,5)$ and $(7,11)$ and is a distance of $3$ units from each of those two points. The point $(7,8)$ is also a distance of $3$ units from $(4,8)$. Because the point $(7,8)$ is the same distance from all three given points, it must be the center of the circle. The radius of a circle is the distance from the center to any point on the circle. Since that distance is $3$, it follows that the radius of the circle is $3$. The circumference of a circle with radius $r$ is equal to $2\pi r$. It follows that the circumference of the circle is $2(\pi )(3)$, or $6\pi$. It's given that the circumference of the circle is $k\pi$. Therefore, the value of $k$ is $6$.